1. M. C. Escher
Victor Vasarely
Op Art
Tessellations
Marjorie Rice

2. What is Tessellations?
A dictionary* will tell you that the word "tessellate" means to form or arrange small squares in a checkered or mosaic pattern.
The word "tessellate" is derived from the Ionic version of the Greek word "tesseres," which in English means "four." The first tiling were made from square tiles.

3. A regular polygon has 3 or 4 or 5 or more sides and angles, all equal.
A regular tessellation means a tessellation made up of congruent regular polygons. [Remember: Regular means that the sides of the polygon are all the same length. Congruent means that the polygons that you put together are all the same size and shape.]

4. We usually add a few more rules to make things interesting!
REGULAR TESSELLATIONS:
RULE #1:   The tessellation must tile a floor (that goes on forever) with no overlapping or gaps.
RULE #2:  The tiles must be regular polygons - and all the same.
RULE #3:   Each vertex must look the same.

5. a tessellation of triangles
Only three regular polygons tessellate in the Euclidean plane: triangles, squares or hexagons. We can't show the entire plane, but imagine that these are pieces taken from planes that have been tiled
Here are examples:
a tessellation of triangles
a tessellation of squares
a tessellation of hexagons

6. Johannes Kepler's Polyhedra

7. 1 Tessellation What's a vertex? Is this a Tessellation Yes or No?
where all the "corners" meet!
Is this a Tessellation
Yes or No?

8. 2
Tessellation
Is this a Tessellation
Yes or No?

9. Tessellation 3
Is this a Tessellation
Yes or No?

10. Tessellation 4
Is this a Tessellation
Yes or No?

11. Tessellation 5 Is this a Tessellation Yes or No?
Basically, a tessellation is a way to tile a floor (that goes on forever) with shapes so that there is no overlapping and no gaps.

12. Tessellation 6
Is this a Tessellation
Yes or No?

13. Tessellation
Yes No